Improved Finite Element Model for Lateral Stability Analysis of Axially Functionally Graded Nonprismatic I-beams

2019 ◽  
Vol 19 (09) ◽  
pp. 1950108 ◽  
Author(s):  
Masoumeh Soltani ◽  
Behrouz Asgarian ◽  
Foudil Mohri
Keyword(s):  
Finite Element ◽  
Power Series ◽  
Material Properties ◽  
Volume Fraction ◽  
Weak Form ◽  
Element Model ◽  
Functionally Graded ◽  
Element Formulation ◽  
Lateral Buckling ◽  
Simply Supported

This paper investigates the lateral buckling of simply supported nonprismatic I-beams with axially varying materials by a novel finite element formulation. The material properties of the beam are assumed to vary continuously through the axis according to the volume fraction of the constituent materials based on an exponential or a power law. The torsion governing equilibrium equation of the simply supported beam with free warping is numerically solved by employing the power series approximation. To this end, all the mechanical properties and displacement components are expanded in terms of the power series to a known degree. Then the shape functions are obtained by representing the deformation shape of the axially functionally graded (AFG) web and/or flanges tapered thin-walled beam in a power series form. At the end, new [Formula: see text] elastic and buckling stiffness matrices are exactly determined from the weak form expression of the governing equation. Three comprehensive examples each of axially nonhomogeneous and homogeneous tapered beams with doubly symmetric I-sections are presented to evaluate the effects of different parameters such as axial variation of material properties, tapering ratio and load height parameters on the lateral buckling strength of the beam. The numerical outcomes of this paper can serve as a benchmark for future studies on lateral-torsional critical loads of AFG beams with varying I-sections.

The Effects of Layer-by-Layer Thickness and Fiber Volume Fraction Variation on the Mechanical Performance of a Pressure Vessel

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Emre Özaslan ◽  
Ali Yetgin ◽  
Bülent Acar ◽  
Volkan Coşkun ◽  
Tarık Olğar
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Material Properties ◽  
Fiber Volume Fraction ◽  
Mechanical Performance ◽  
Volume Fraction ◽  
Element Model ◽  
Layer By Layer ◽  
Fiber Volume ◽  
Filament Wound

Abstract Due to high stiffness/weight ratio, composite materials are widely used in aerospace applications such as motor case of rockets which can be regarded as a pressure vessel. The most commonly used method to manufacture pressure vessels is the wet filament winding. However, the mechanical performance of a filament wound pressure vessel directly depends on the manufacturing process, manufacturing site environmental condition, and material properties of matrix and fiber. The designed pressure vessel may not be manufactured because of the mentioned issues. Therefore, manufacturing of filament wound composite structures are based on manufacturing experience and experiment. In this study, effects of layer-by-layer thickness and fiber volume fraction variation due to manufacturing process on the mechanical performance were investigated for filament wound pressure vessel with unequal dome openings. First, the finite element model was created for designed thickness dimensions and constant material properties for all layers. Then, the model was updated. The updated finite element model considered the thickness of each layer separately and variation of fiber volume fraction between the layers. Effects of the thickness and fiber volume fraction on the stress distribution along the motor axial direction were shown. Also hydrostatic pressurization tests were performed to verify finite element analysis in terms of fiber direction strain through the motor case outer surface. Important aspects of analyzing a filament wound pressure vessel were addressed for designers.

BUCKLING ANALYSIS OF FUNCTIONALLY GRADED SKEW PLATES: AN EFFICIENT FINITE ELEMENT APPROACH

2013 ◽  
Vol 05 (04) ◽  
pp. 1350041 ◽  
Author(s):  
M.N.A. GULSHAN TAJ ◽  
ANUPAM CHAKRABARTI
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Element Formulation ◽  
Skew Angle ◽  
Buckling Behavior ◽  
Metal Plates ◽  
Graded Material

In the present study, an attempt has been made to present the Co finite element formulation based on third order shear deformation theory for buckling analysis of functionally graded material skew plate under thermo-mechanical environment. Here, prime emphasis has been given to study the influence of skew angle on the buckling behavior of functionally graded plate. Two dissimilar homogenization schemes, namely Mori–Tanaka scheme and Voigt rule of mixture are employed to sketch their influence for the interpretation of data. Temperature-dependent material properties of the constituents of the plate are considered to perform thermal analysis. Numerical examples are solved using different mixture of ceramic and metal plates to generate the new results and relative imperative conclusions are highlighted. The roles played by the different factors like loading condition, volume fraction index, skew angle, boundary condition, aspect ratio, thickness ratio and homogenization schemes on buckling behavior of the FGM skew plates are presented in the form of tables and figures.

Nonlinear transient and thermal analysis of functionally graded shells using a seven-parameter shell finite element

2017 ◽  
Vol 1 (2) ◽  
Author(s):  
Miguel Gutierrez Rivera ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Mechanical Response ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Shell Element ◽  
Element Model ◽  
Functionally Graded ◽  
Plates And Shells ◽  
Shell Finite Element ◽  
Transient Thermal

AbstractIn this paper the thermo-mechanical response of functionally graded plates and shells is studied using a continuum shell finite element model with high-order spectral/hp basis functions. The shell element is based on the seven-parameter first-order shear deformation theory, and it does not utilize reduced integration or stabilization ideas and yet exhibits no locking. The static and dynamic response of functionally graded shells, with power-law variation of the constituents, under mechanical and thermal loads is investigated by varying the volume fraction of the constituents. Numerical results for deflections and stresses are presented and compared with available analytical and finite element results from the literature. The performance of the shell element for transient thermal problems is found to be excellent.

Effect of porosity and skew edges on transient response of functionally graded sandwich plates

2021 ◽  
pp. 030932472110626
Author(s):  
Abhilash Karakoti ◽  
Mahesh Podishetty ◽  
Shashank Pandey ◽  
Vishesh Ranjan Kar
Keyword(s):  
Finite Element ◽  
Transient Response ◽  
Volume Fraction ◽  
Pure Metal ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Skew Angle ◽  
Wide Range

This work for the first time presents the effect of porosity and skew edges on the transient response of functionally graded material (FGM) sandwich plates using a layerwise finite element formulation. Two configurations of FGM sandwich plates are considered. In the first configuration, the top and the bottom layers are made of the FGM and the core is made of pure metal, whereas in the second configuration, the bottom, core and the top layers are made of pure metal, FGM and pure ceramic, respectively. Four micromechanics models based on the rule of mixture are used to model porosity for these two configurations of FGM sandwich plates. A layerwise theory based on a first-order shear deformation theory for each layer that maintains the displacement continuity at the layer interface is used for the present investigation. An eight-noded isoparametric element with nine degrees of freedom per node is used to develop the finite element model (FEM). The governing equations for the present investigation are derived using Hamilton’s principle. A wide range of comparison studies are presented to establish the accuracy of the present FEM formulation. It has been shown here that the parameters like skew angle, porosity coefficient, volume fraction index, core to facesheet thickness ratio and boundary conditions have a significant effect on the transient response of FGM sandwich plates. Also, the present finite element formulation is simple and accurate.

scholarly journals A Finite Element Formulation and Nonlocal Theory for the Static and Free Vibration Analysis of the Sandwich Functionally Graded Nanoplates Resting on Elastic Foundation

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Van-Ke Tran ◽  
Thanh-Trung Tran ◽  
Minh-Van Phung ◽  
Quoc-Hoa Pham ◽  
Trung Nguyen-Thoi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Material Properties ◽  
Free Vibration Analysis ◽  
Nonlocal Theory ◽  
Functionally Graded ◽  
Element Formulation ◽  
Proposed Model ◽  
Homogeneous Core

This article presents a finite element method (FEM) integrated with the nonlocal theory for analysis of the static bending and free vibration of the sandwich functionally graded (FG) nanoplates resting on the elastic foundation (EF). Material properties of nanoplates are assumed to vary through thickness following two types (Type A with homogeneous core and FG material for upper and lower layers and Type B with FG material core and homogeneous materials for upper and lower layers). In this study, the formulation of the four-node quadrilateral element based on the mixed interpolation of tensorial components (MITC4) is used to avoid “the shear-locking” problem. On the basis of Hamilton’s principle and the nonlocal theory, the governing equations for the sandwich FG nanoplates are derived. The results of the proposed model are compared with published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and material properties on the static and free vibration behaviors of nanoplates are investigated in detail.

Buckling of Simply Supported Piezoelectric FGM Plates Subjected to Electro-Mechanical Loading Using Higher-Order Shear Deformation Theory

2012 ◽  
Vol 622-623 ◽  
pp. 200-205
Author(s):  
Kamal M. Bajoria ◽  
Priyanka A. Jadhav
Keyword(s):  
Stability Analysis ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Deformation Theory ◽  
Piezoelectric Effect ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Simply Supported ◽  
Graded Material

This paper investigates the stability analysis of plates made of functionally graded material (FGM) and integrated with piezoelectric actuator and sensor at top and bottom face subjected to electrical and mechanical loading. The finite element formulation is presented using degenerated shell element, von-Karman hypothesis, higher-order shear deformation theory and considering the piezoelectric effect. The governing equilibrium equation is derived using the principle of minimum energy and solution for critical buckling load is obtained by solving Eigen value problem. The material properties of the FGM plates are assumed to be graded along the thickness direction according to simple power-law distribution in terms of the volume fraction of the constituents, while the poison’s ratio is assumed to be constant. Stability analysis is carried out on simply supported plate made of newly introduced metal based functionally graded material (FGM) i.e. mixture of aluminum and stainless steel which exhibits the two different material properties in single material i.e. high corrosion resistance as well as high strength. Results show that the buckling strength of plate increases with increase in volume fraction indices through the thickness and it can be further improved with the help of piezoelectric effect.

scholarly journals Finite Element Model for Free Vibration Analyses of FG-CNT Reinforced Composite Beams using Refined Shear Deformation Theories

2021 ◽  
Vol 1206 (1) ◽  
pp. 012019
Author(s):  
Surojit Biswas ◽  
Priyankar Datta
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Distribution Type

Abstract The present article deals with the free vibration of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams employing various refined deformation theories and validates the accuracy and feasibility of these proposed theories. The theories involved are the first order shear deformation theory (FSDT) and other refined theories involving additional higher order terms. Carbon nanotubes (CNTs) are assumed to be oriented along the axis of the beam. Uniform and three types of different functionally graded (FG) distributions of CNTs through the thickness of the beam are considered. The rule of mixture is used to describe the effective material properties of the beams. The governing equations are derived using Hamilton’s principle and solved using the finite element method (FEM). A FEM code is compiled in MATLAB considering a C 0 finite element. The influences of different key parameters such as CNT volume fraction, distribution type of CNTs, boundary conditions and slenderness ratio on the natural frequencies of FG-CNTRC beams are investigated. It can be concluded that the above-mentioned parameters have significant influence on the free vibration of the beam and the accuracy of the proposed refined theories is good.

Layer-wise finite-element analysis of a functionally graded hollow thick cylinder with a piezoelectric ring

2011 ◽  
Vol 225 (5) ◽  
pp. 1045-1060 ◽  
Author(s):  
M H Yas ◽  
M Shakeri ◽  
M Khanjani
Keyword(s):  
Finite Element ◽  
Potential Energy ◽  
Virtual Work ◽  
Electrical Potential ◽  
Element Model ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Element Formulation ◽  
Element Analysis ◽  
Thick Cylinder

In this work, a layer-wise finite-element formulation is developed for the analysis of a functionally graded material (FGM) hollow thick cylinder with one piezoactuator ring. The cylinder and ring is divided into many sublayers in the thickness direction and the full layer-wise shell theory is used to model a discretely stiffened FGM cylinder. In this model, the displacements are approximated linearly through each mathematical layer. This accounts for any discontinuities in the derivatives of the displacement at the interface of the ring and the cylindrical thick shell. This formulation is derived from the virtual work statement which includes the total structural potential energy and the electrical potential energy of the piezoelectric ring. Assembling stiffness and mass matrices, at each interface between two elements, stress and displacement continuity are forced, and then the finite-element model is solved. Static and dynamic responses of a functionally graded thick cylinder to electrical and mechanical loads with different exponent ‘ n’ of FGM are determined to show the significant influence of the material in homogeneity. The results obtained at a distance far from the ring are compared with the mechanical behaviour of an FGM cylindrical shell without a ring. Because of the Saint Venant effects, the piezoelectrically induced deformation of the shell is confined to a region close to the piezoelectric ring; thus agreements between these two results are observed.

Vibration of Initially Stressed Functionally Graded Material Plates and Shells

2014 ◽  
Vol 684 ◽  
pp. 158-164 ◽  
Author(s):  
Sugirtha Singh J. Monslin ◽  
Thangaratnam R. Kari
Keyword(s):  
Finite Element ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Shell Element ◽  
Functionally Graded ◽  
Element Formulation ◽  
Vibration Frequencies ◽  
Functionally Graded Plates ◽  
Graded Material ◽  
Plates And Shells

Finite element formulation using semiloof shell element for initially stressed vibration of Functionally Graded Material (FGM) plates and shells are presented. The influence of volume fraction index on the vibration frequencies of thin functionally graded plates and shells and variation of temperature on frequency are studied. New results are presented for initially stressed vibration of FGM plates and shells.

scholarly journals Large displacements of FGSW beams in thermal environment using a finite element formulation

2020 ◽  
Author(s):  
Bui Thi Thu Hoai ◽  
Nguyen Dinh Kien ◽  
Tran Thi Thu Huong ◽  
Le Thi Ngoc Anh
Keyword(s):  
Finite Element ◽  
Temperature Rise ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Effect Of Temperature ◽  
Element Formulation ◽  
Beam Model ◽  
Large Displacements

The large displacements of functionally graded sandwich (FGSW) beams in thermal environment  are studied using a finite element formulation. The beams are composed of three layers, a homogeneous core and two functionally graded face sheets with volume fraction of constituents following a power gradation law. The material properties of the beams are considered to be temperature-dependent.  Based on Antman beam model and the total Lagrange formulation, a two-node nonlinear beam element taking the effect of temperature rise into account  is formulated and employed in the study. The element with explicit expressions for the internal force vector and tangent stiffness matrix is derived using linear interpolations and reduced integration technique to avoid the shear locking. Newton-Raphson based iterative algorithm is employed in combination with the arc-length control method to compute the large displacement response of a cantilever FGSW beam subjected to end forces.  The accuracy of the formulated element is confirmed through a comparison study. The effects of the material inhomogeneity, temperature rise and layer thickness ratio on the large deflection response of the beam are examined and highlighted.

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